EE 603 Power Electronics

Homework # 1 Due January 18, 2006

In Mohn/Underland/Robbins browse chapters 1 and 2. Read in chapter 2 sections 2.2, 2.4, 2.6, and 2.8. Start reading chapter 7.

Problem 1

Vin is a sinewave with a peak value Vp

a) Sketch V_f, Vout, and i_f for one complete cycle of Vin. Label your sketches showing the time relationship between the various waveforms.

b) Compute the average and rms values of Vin, i_f and Vout.

c) Sketch the power in the resistor.

d) What is the average power in the resistor?

Problem 2

Vin is a sinewave with a peak value Vp

a) Sketch Vout for one complete cycle of Vin.

b) Compute the average and rms values of Vout.

c) Sketch the power in the resistor.

d) What is the average power in the resistor?

Problem 3

a) What is Vout in terms of Vin, R1 and R2?

b) Assume R1 << R2. Expand your answer from part a) in a Taylor series about the point R1 = 0W stopping at the R1³ term.

c) What is the approximate value of Vout if R1 = 0W?

d) Using your approximate Vout from part c), what is the current equal to?

e) Now that you have an approximate value of the current, you can obtain a more accurate estimate of Vout. Using your current from part d), what is the voltage across R1 (no longer assume it is zero) and what is a better estimate of Vout?

f) Using your better estimate of Vout from part e), what is a better estimate of the current?

g) Using your better estimate of the current from part f), what is a better estimate of the voltage across R1 and thus R2?

h) Repeat the process in f) and g) getting better and better estimates of Vout. Do this until you get an R3 term. At this point compare your estimate of Vout using the iterative method outlined in c) through g) to the Taylor series result. Comment.

Problem 4

The family of characteristic curves for a particular MOSFET is shown below. The drain current in amps is plotted versus the drain to source voltage in volts for gate voltages going from zero volts to 7V in one volt steps. The MOSFET is used in the circuit also shown below. The input voltage is 5V. You may detach the MOSFET’s characteristic curves and hand them in with your solution.

a) Label the triode region and the saturated region on the plot. Indicate the boundary between the triode region and the saturated region.

b) Estimate the MOSFET’s threshold voltage. Note that there are two ways to make this estimate.

c) Estimate the value of Kp for the MOSFET. Be sure to give Kp’s units.

d) For the above circuit, plot the circuit’s load line (solve the problem graphically) on the MOSFET’s characteristic curves. Numerically label the x and y axis intercepts and the slope of the line.

e) For the circuit above, what is V_DS and I_D when the input voltage Vin is equal to 5V? Indicate the circuit’s operating point on your plot. You can obtain V_DS and I_D from your graph or analytically. Graphical accuracy is adequate.

f) When Vin is changed to 7V, what is the value of V_DS and I_D? Indicate the circuit’s new operating point on your plot. You can obtain V_DS and I_D from your graph. Graphical accuracy is adequate.

g) When Vin is changed to 1V what is V_DS and I_D? When Vin is changed to 15V what is V_DS and I_D?